f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ) 求 ①f(θ)的定义域 ②化简f(θ)的表达式③若f(θ)=1/2,求tanθ sinθ cosθ
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![f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ) 求 ①f(θ)的定义域 ②化简f(θ)的表达式③若f(θ)=1/2,求tanθ sinθ cosθ](/uploads/image/z/2624923-19-3.jpg?t=f%28%CE%B8%29%3D%5Bsin%283%CF%80-%CE%B8%29cos%28%CF%80%2F2%2B%CE%B8%29%5D%2Ftan%28%CF%80-%CE%B8%29+%E6%B1%82+%E2%91%A0f%EF%BC%88%CE%B8%EF%BC%89%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F+%E2%91%A1%E5%8C%96%E7%AE%80f%EF%BC%88%CE%B8%EF%BC%89%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F%E2%91%A2%E8%8B%A5f%EF%BC%88%CE%B8%EF%BC%89%3D1%2F2%2C%E6%B1%82tan%CE%B8+sin%CE%B8+cos%CE%B8)
f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ) 求 ①f(θ)的定义域 ②化简f(θ)的表达式③若f(θ)=1/2,求tanθ sinθ cosθ
f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ) 求 ①f(θ)的定义域 ②化简f(θ)的表达式
③若f(θ)=1/2,求tanθ sinθ cosθ
f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ) 求 ①f(θ)的定义域 ②化简f(θ)的表达式③若f(θ)=1/2,求tanθ sinθ cosθ
f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ)=sinθcos(π/2-θ)/tanθ=sin²θ/tanθ
(1)tanθ≠0 ∴θ≠kπ且θ≠kπ+π/2
(2)f(θ)=sin²θ/tanθ=sinθcosθ=1/2 sin2θ
(3))f(θ)=1/2 ∴sin2θ=1 ∴2θ=2kπ+π/2 ∴θ=kπ+π/4
∴tanθ=tan(kπ+π/4)=tan(π/4)=1
sinθ=sin(kπ+π/4)=±√2/2
cosθ=cos(kπ+π/4)=±√2/2